Abstract
Iterated Tikhonov regularization can be seen as an iterative refinement of an initial solution obtained by applying the standard Tikhonov regularization. This kind of approach is particularly suited when noisy data with low signal-to-noise ratio (SNR) are to be used. However, to apply such an approach, an initial regularization parameter has to be estimated. Generally, it is obtained numerically through automatic selection procedures that can require intensive computations. In this respect, the multiplicative regularization is an interesting alternative, since it does not require any selection procedure for choosing the regularization parameter. In return, the amount of reg-ularization is automatically adjusted throughout an iterative resolution process. To combine the best of both worlds for solving force reconstruction problems, we propose a stationary iterated multiplicative regularization that allows using prior information on the type of sources acting on the structure. The validity and the suitability of the proposed approach are illustrated numerically on a free-free beam excited by a point force.
Mathieu Aucejo
Associate Professor
My research interests include inverse problems, vibration control and vibro-acoustics.